"Relations will be broken" unless Israel apologizes or accepts the conclusions of an international inquiry into the May 31 attack on the Gaza-bound flotilla, he told Monday's edition of the Hurriyet newspaper.
Turkey has until now called for an international probe into the raid but in a break with that position, Davutoglu did not reject the creation of Israel's own commission to investigate the raid.
"If this commission concludes that the raid was unjust and if they apologize, that will be sufficient," he said, although he insisted that Turkey wanted compensation from the Jewish state.
Despite Davutoglu's meeting with Israeli Minister of Industry, Trade and Labor Binyamin Ben-Eliezer, the Turkish stance remains firm. "We showed them the way out. If they apologize as a result of the probe that they are carrying out themselves, this will be sufficient. But of course, we must first see this."
The Turkish foreign minister went on to say, "They are aware of our demands. If they do not agree to apologize, they must agree to an international inquiry."
Davutoglu said he wants ties between Turkey and Israel to be restored to the way they were before the raid. He said his country would like to give a chance to countries interested in rehabilitating Ankara's ties with Jerusalem, hinting at American involvement.
On his meeting with Israeli Minister Binyamin Ben-Eliezer, he said, "Make no mistake. The meeting with Ben-Eliezer was not held under the United State's mediation. We briefed Barack Obama on this meeting at the G-20 summit in Toronto."
He stressed that he met with Ben-Eliezer as "Netanyahu's special envoy".
He said the decision came a week after the raid. When asked, he said the ban may be expanded to include civilian flights.
In conclusion, the Turkish foreign minister said that if Israel does not take the necessary steps, "the isolation process will continue." He said, "We know what we want. We are right in our means. We will continue in this path until our demands are met."
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